Application of the ECM algorithm to the estimation of the likelihood function in financial auditing

• Autorzy: Sitek Grzegorz

Identyfikatory

DOI

10.29119/1641-3466.2024.198.26

• Języki publikacji: EN

Abstrakty

EN

Purpose: The book amounts are treated as values of a random variable whose distribution is a mixture of the distributions of the correct amount and the true amount contaminated by error. The mixing coefficient is equal to the proportion of the items with non-zero errors amounts. Below we consider a problem of testing appropriately formulated statistical hypotheses about admissibility of the total or the mean accounting errors. Hypotheses can be verified by the likelihood ratio test. In this paper, we show how to estimate parameters of the likelihood function. Design/methodology/approach: The book amounts are treated as values of a random variable whose distribution is a mixture of the distributions of the correct amount and the true amount contaminated by error. The mixing coefficient is equal to the proportion of the items with non- zero errors amounts. Below we consider a problem of testing appropriately formulated statistical hypotheses about admissibility of the total or the mean accounting errors. Hypotheses can be verified by the likelihood ratio test. In this paper, we show how to estimate parameters of the likelihood function. Findings: The work presents formulas for the parameters of the likelihood function. These parameters were obtained using the ECM algorithm. Originality/value: The problem of estimating the average audit error is very common in economic research. A method for estimating the average audit error based on the likelihood function was proposed. The parameters of the likelihood function were estimated using the ECM algorithm.

Słowa kluczowe

EN

ECM algorithm; likelihood ratio test; mixture of probability distribution

PL

algorytm ECM; test ilorazu wiarygodności; mieszanina rozkładów prawdopodobieństwa

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska
• Rocznik: 2024
• Tom: z. 198
• Strony: 475--487
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Sitek Grzegorz

• Uniwersytet Ekonomiczny w Katowicach, Katedra Statystyki, Ekonometrii i Matematyki

• https://orcid.org/0000-0002-7191-8631

Bibliografia

• 1. Frost, P.A., Tamura, H. (1986). Accuracy of auxiliary information interval estimation in statistical auditing. Journal of Accounting Research, 24, 57-75.
• 2. Kaplan, R.S. (1973). Statistical Sampling in Auditing with Auxiliary Information Estimators. Journal of Accounting Research, 238-258.
• 3. McLachlan, G., Peel, D. (2000). Finite Mixture Models. New York: Wiley.
• 4. Meng, X.L., Rubin, D.B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80, 267-278.
• 5. Silvey, S.D. (1959). The Lagrangian multiplier test. The Annals of Mathematical Statistics, 30, 2, 389-407.
• 6. Stringer, K.W. (1963). Practical Aspects of Statistical Auditing. Preceeding of Business and Economic Statistics Section of the American Statistical Association, 405-411.
• 7. Tamura, H. (1988). Estimation of rare errors using judgement. Biometrika, 75, 1-9.
• 8. Wywiał, J.L. (2016). Contributions to Testing Statistical Hypotheses in Auditing. Warsaw: PWN, 91-95.
• 9. Wywiał, J.L. (2018). Application of two gamma distributions mixture to financial auditing. Sankhyã B: The Indian Journal of Statistics.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).